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Linear Regressions
A regression is a process that takes all the points and calculates the equation that best 'fits' those points. A linear regression simply means that the equation will be the equation of a line.
Examples of Linear Regressions and Graphs
Look at the both sets of points pictured below. What is the equation of the line that 'best fits' each set of points?
In both case, the line of best fit is the y = x. As you can see from both graphs, this equation is a better fit for the first set of points but it still fits the 2nd set pretty well.
| 1st set of points |
2nd Set of points |
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Practice Problems
Practice Problem 1) The table below represents the coordiantes of points. Calculate the linear regression that best fits the points below. (Note:these problems assume that you are using a graphing calculator to calculate the linear regression)
| Show equation of linear regression |
| X |
Y |
| 5 |
9 |
| 6 |
9.25 |
| 7 |
9.5 |
| 8 |
9.75 |
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The linear regression that best fits these points is the equation
y = ¼x +7.75
Now, using this equation what is the y value when x = 54?
Substitute x = 54 into the linear regression equation that you just found
y = ¼x + 7.5
y = ¼(54) + 7.5
y = 21
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Practice problem 2)
The accompanying table shows the enrollment of a preschool from 1980 through 2000. Write a linear regression equation to model the data in the table. Predict what the enrollment will be in the year 2010
| Show equation of linear regression |
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The lineaer regression that best fits these points is the equation
y = 1.08x − 2125
Now, using this equation what is the y value when x = 2010?
Substitute x = 2010 into the linear regression equation that you just found
y = 1.08(x) − 2125
y = 1.08(2010) − 2125
y = 55
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